Subgroups — C₃×#470 #5344

Order 192.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₃×C₂²⋊Q₈	C₂	1	2	yes	maximal
4	C₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#103	C₂	1	2	yes	maximal, complemented
6	#470	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂×C₃×Q₈	C₂²	1	2	yes	—
8	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
9	C₃×Q₁₆	—	2	2	no	—
10	C₃×M₁₆	—	2	2	no	—
11	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
13	C₃×C₄⋊C₄	—	2	2	no	—
14	C₃×C₄⋊C₄	C₂²	1	2	yes	—
15	C₃×C₂²⋊C₄	—	2	2	no	—
16	C₂×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
17	C₂×M₁₆	C₂×C₃	1	1	yes	characteristic
18	C₂²⋊Q₈	C₂×C₃	1	2	yes	—
19	#106	C₂×C₃	1	1	yes	characteristic, complemented
20	#103	C₂×C₃	1	2	yes	complemented
21	C₂³×C₃	D₄	1	1	yes	characteristic
22	C₃×Q₈	—	2	2	no	—
23	C₃×Q₈	—	2	2	no	—
24	C₂×C₃×C₄	—	2	1	no	—
25	C₂×C₃×C₄	—	2	1	no	—
26	C₂×C₃×C₄	—	2	2	no	—
27	C₂×C₃×C₄	—	2	2	no	—
28	C₂×C₃×C₄	D₄	1	1	yes	characteristic
29	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
30	C₃×C₈	—	2	1	no	—
31	C₃×C₈	D₄	1	2	yes	—
32	C₂×Q₈	C₂²×C₃	1	2	yes	—
33	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
34	Q₁₆	—	2	2	no	—
35	M₁₆	—	2	2	no	—
36	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
37	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
38	C₄⋊C₄	—	2	2	no	—
39	C₄⋊C₄	C₂²×C₃	1	2	yes	—
40	C₂²⋊C₄	—	2	2	no	—
41	C₂²×C₃	—	2	1	no	—
42	C₂²×C₃	—	2	2	no	—
43	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
44	C₃×C₄	—	2	1	no	—
45	C₃×C₄	—	4	2	no	—
46	C₃×C₄	—	4	2	no	—
47	C₃×C₄	C₂×D₄	1	1	yes	characteristic
48	C₃×C₄	#41	1	1	yes	characteristic
49	C₂³	C₃×D₄	1	1	yes	characteristic
50	Q₈	—	2	2	no	—
51	Q₈	—	2	2	no	—
52	C₂×C₄	—	2	1	no	—
53	C₂×C₄	—	2	1	no	—
54	C₂×C₄	—	2	2	no	—
55	C₂×C₄	—	2	2	no	—
56	C₂×C₄	C₃×D₄	1	1	yes	characteristic
57	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
58	C₈	—	2	1	no	—
59	C₈	C₃×D₄	1	2	yes	—
60	C₂×C₃	—	4	1	no	—
61	C₂×C₃	#121	1	1	yes	characteristic
62	C₂×C₃	#137	1	2	yes	—
63	C₂²	—	2	1	no	—
64	C₂²	—	2	2	no	—
65	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
66	C₄	—	2	1	no	—
67	C₄	—	4	2	no	—
68	C₄	—	4	2	no	—
69	C₄	C₂×C₃×D₄	1	1	yes	characteristic
70	C₄	C₃×#41	1	1	yes	characteristic
71	C₃	#470	1	1	yes	characteristic, direct product factor, Sylow
72	C₂	—	4	1	no	—
73	C₂	C₃×#121	1	1	yes	characteristic
74	C₂	C₃×#137	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₃
prime radical	C₂³×C₃	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₃×Q₁₆	C₂	semidirect
4. C₃×#106	C₂	semidirect
5. C₃×#103	C₂	semidirect
6. #470	C₃	direct (N × H)
16. C₂×Q₁₆	C₂×C₃	semidirect
19. #106	C₂×C₃	semidirect
20. #103	C₂×C₃	semidirect
71. C₃	#470	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×Q₁₆	2
C₂×C₃×M₁₆	2
C₃×C₂²⋊Q₈	2
C₃×#106	2
C₃×#103	2
#470	3

Subgroups — C3×#470 #5344

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#470 #5344